光镊技术中的纳米位移探测及其测量误差讨论

光镊系统可以实现微米粒子的纳米精度位移测量，对该测量装置和方法及各种误差来源进行了分析。着重讨论了动态图像分析法，包括灰度重心法和新发展的幂次重心法、二次曲线拟合法。提出了一种对图像分析法边行评估的数值模拟方法，对这三种算法引起的误差进行了数值模拟。结果表明，方法误差与随机噪声的性质有关：在本底噪声为主时，二次曲线拟合法精度高，计算量小。用四像限探测器和图像分析法对固定的微米小球进行了位置测量，二者的标准偏差分别为1nm和0．3nm。在纳米精度的位移测量的基础上，可以实现光阱刚度的测量，并进而测量了微米小球所受到的亚皮牛顿力。基于位移和刚度的精密测量，微小力的测量可以达到飞牛顿量级。

Detection of Nanometer Displacement in Optical-Tweezers and Its Related Measuring Errors

Optical Tweezers can be used in measuring nanometer displacements of a particle with several micron diameters. Methods of measurement and data processing, error sources are analyzed. The dynamic image analysis methods including the gray centroid method and new developed methods: exponent centroid method and parabolic fit method are discussed and compared. A numerical simulation method was developed to evaluate errors caused by these different methods and compared the errors of three data processing methods. The result shows that the parabolic fit method has a high precision with fewer computing time when the background noise is the main noise source. The position of a fixed particle is measured by the quadrant detect (QD) method and the dynamic image analysis method. The measurement standard deviation is 1 nm and 0.3 nm respectively. Based on nanometer displacement measurement, the trap stiffness can be got. Finally, a sub-PicoNewton external force which is applied on the particle is measured successfully. It shows that the resolution of force measurement can reach femto Newton order.